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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 68: 225-232 (1985)
Computed Tomography and Automated Image Analysis of
Prehistoric Femora
DALE R. SUMNER, BRENT MOCKBEE, KATHLEEN MORSE,
THOMAS CRAM, AND MICHAEL PITT
Department of Orthopedic Surgery, Rush Presbyterian St. Luke’s Medical
Center (0.R.S.), Chicago, Illinois 60612, Department of Radiology (B.M.,
M.P.), University of Arizona, Tucson, Arizona 85724, and Interactive
Graphics Engineering Laboratory (K.M., TC.), University ofArizona,
Tucson, Arizona 85721
KEY WORDS Femur, Cross-sectional geometry, Biomechanics,
Computed tomography, Morphology
ABSTRACT
Non-invasive characterization of limb bone cross-sectional geometry would be useful for biomechanical analyses of skeletal collections.
Computed tomography (CT) is potentially the method of choice. Additionally,
CT images are suitable for automated analysis. CT is here shown to be both
accurate and precise in the analysis of cross-sectional geometry of prehistoric
femora. Beam hardening artifacts can be reduced by using a water bath. As
the availability of CT for research increases, both bone density and geometry
could be determined simultaneously with this method.
Biomechanical analysis of skeletal morphology is becoming more common in anthropology. Characterization of long bone crosssectional geometry is critical to this approach. Cross-sectional geometry has now
been studied in humans (Ruffand Hayes,
1983a; 1983b; and references cited therein),
non-human primates (Burr et al., 1981; 1982)
and in other species (Rybicki et al., 1977;
Piotrowski et al., 1983).
Cross-sectional geometric properties of relevance to biomechanics include cortical area,
area moments of inertia and the position of
the principal axes (Fig. 1).The spatial distribution of bone tissue can also be quantified
by constructing two ratios: IXAY and IMAW
IMIN. The biomechanical significance of
these properties has been discussed previously in the anthropology literature (see references cited above).
Anthropologists are interested in variability and because of their access to large skeletal collections have the ability to assess the
effects of factors such as age and sex on intrapopulational variability. This approach has
been particularly useful in the analysis of
changes in cross-sectional geometry associated with aging. For instance, Ruff and
Hayes (1982) were able to corroborate the
hypothesis of Smith and Walker (1964) that
0 1985 ALAN R. LISS, INC.
subperiosteal expansion compensates for loss
of bone mineral in aging in males and
females.
Studies of cross-sectional geometry are restricted by the limited number of skeletal
samples which can be physically sectioned.
Non-destructive methods of skeletal analysis
include radiogrammetry, photon absorptiometry and computed tomography. Radiogrammetry has well-known limitations (Cohn,
1981). Photon absorptiometry has been
adapted to calculating the cross-sectional moment of inertia about the anteroposterior and
mediolateral axes (Martin and Burr, 1984).
This technique is non-invasive and potentially accessible to many researchers. A disadvantage is that not all aspects of the bone’s
cross-sectional geometry are available. Cortical area and medullary area can be determined, but the location of the principal axes
and the magnitude of the moments of inertia
about these axes remain unknown. Computed tomography (CT) appears to be the
method of choice.
Computed tomography is well-suited to
quantitative morphology (Robb, 1982; Tate
and Cann, 1982).The basic principle of CT is
Received November 28, 1984; revised May 3, 1985; accepted
May 22, 1985.
226
D.R. SUMNER ET AL.
Ix = f y 2 d A
A
Iy = jx2dA
Ixy =
/xydA
J = jr2dA
IP
B
IA
major axis
IMAX =
7
7
lYtlX
-k
Ixy2t-!-(Iy- Ix)
minor axis
IP
Fig. 1. Cross-sectional geometry. A) Second moments
of area about the AP (IX) and ML (IY) axes, the cross
product (IXY) and the polar moment of inertia (3.B)
Location of the principal axes and formulae used to cal-
culate the maximum (IMAX) and minimum (MMIN)principal second moments of area. Redrawn after Martin and
Atkinson (1977) and Nagurka and Hayes (1980).
that with multiple angular projections “the
amount of attenuation of each square of tissue can be calculated knowing only the
amount of attenuation of the beam as it
passes completely through the body” (Winter
and King, 1983:8). In most commercially
available scanners a n X-ray tube is rotated
around the body, numerous projections are
obtained and mathematical techniques are
used to reconstruct a cross-sectional image
(Robb, 1982). The image is called a slice, but
actually represents the distribution of X-ray
attenuation in a series of volume elements
(voxels). The computer stores a “CT number”
for each voxel. These numbers are assigned
values on a grey scale and the image can,
therefore, be displayed on a monitor.
CT images of dense objects may be distorted due to beam hardening. Beam hardening refers to preferential absorption of the
lower energy X-rays of the polyenergetic
beam (Robb, 1982). The beam, therefore, becomes more penetrating as it passes through
a n object. Beam hardening is linear for soft
tissues, but is nonlinear for dense objects
such as bone. Reconstruction software can
correct for some of the beam hardening
distortion.
The purpose of the present paper is to describe our application of CT to the study of
cross-sectional geometry in prehistoric femora. In particular, use of a water bath to
reduce beam hardening artifacts and the advantage of automated image analysis for enhancing precision are documented.
MATERIALS AND METHODS
The approach reported here couples automated image analysis with CT (Fig. 2). Three
phases of data collection and reduction are
recognized. Digital images are obtained with
CT. These images are then processed and the
data are reduced to a series of x,y coordinates
which describe the subperiosteal and endosteal perimeters. Each image could be characterized in a number of ways. Here, the
emphasis is on the cross-sectional properties
described in the Introduction. Two experiments were done. First, the effect of beam
hardening on accuracy was determined. Second, the precision of a n automated image
analysis protocol was assessed.
CT AND CROSS-SECTIONAL GEOMETRY
Digital image
Processing
Computed
Tomography
227
Image
Characterization
MFlNlTlON
IMAGES
COORDINATES
CROSS-SECTIONAL
GEOMETRY
Fig. 2. Scheme of the analysis system.
Scan technique
A General Electric CTPT 8800 whole body
scanner was used. The bones were scanned
using 320 mPA, a tube potential of 120 kVp,
576 views per slice and a slice thickness of
1.5 mm. The images were reconstructed with
the “bone” algorithm and, when analyzed on
the CT monitor, a window level of 100 and a
window width of 1,000 were used.
Archaeologically derived whole femora and
diaphyseal segments were placed in a plexiglass box filled with water (except a s noted
below). Each intact femur was set in a standard position and sampled at 20%) 35%)50%)
65%, and 80% of its diaphyseal length. The
diaphyseal segments were oriented in a n
analogous fashion and one image was obtained from each segment. All slices were
obtained perpendicular to the long axis of the
diaphysis.
Digital image processing
We developed a n outlining routine for automated tracing of the subperiosteal and endosteal borders (following Keller et al., 1981).
Although the outlining algorithm itself is
strictly deterministic, neither Keller et al.’s
method for generating the seed pixel nor ours
is deterministic. Our method uses a root
mean square calculation of a region known
to be in the water bath to find the threshold
CT value required by the outlining algorithm. Localization in the transverse plane
and scaling were achieved by interactively
locating the inside corners of the water box
with the cursor on the monitor. The location
of the slice in the longitudinal sense was
known from the CT position indicator.
Image characterization
Cross-sectional image analyses were done
on the CT monitor or with a Vicom digital im-
age processor. The CT monitor was used to
measure subperiosteal and endosteal diameters. The image processor was used for measuring the geometric properties described
above, using the automatic outlining algorithm to define the bone’s edges. The x,y coordinates of the subperiosteal and endosteal
boundaries were supplied to the “SLICE”
computer program (Nagurka and Hayes,
1980) which calculated the cross-sectional
geometric properties shown in Figure 1.
Accuracy (beam hardening experiment)
An experiment was performed to determine if a water bath were necessary to improve accuracy (i.e., reduce beam hardening
artifacts) and, if so, to assess the effects of
differential filling of the medullary cavity
with water. Six diaphyseal segments from
skeletally mature prehistoric femora of unknown provenience were scanned under
three conditions: 1)in air, 2) in a water bath,
but with no water in the medullary cavity,
and 3) in a water bath with water in the
medullary cavity. The segments were not repositioned between scans. Modelling clay
caps were used to obstruct the medullary
cavity during the first two scans. These caps
were carefully removed before the third scan.
Subperiosteal and endosteal anteroposterior
(AP) and mediolateral (ML) diameters were
measured interactively on the CT monitor
using software for measuring distances within images and on the actual specimens with
a Helios dial caliper. In addition, the crosssectional geometric properties described in
Figure 1 were calculated and compared for
the latter two scan conditions.
Precision experiments
Two precision experiments were performed. First, for each of 28 individuals used
in a growth and aging study (Sumner, 1984),
228
A
B
Figure 3.
229
CT AND CROSS-SECTIONAL GEOMETRY
C
Fig. 3. An AP diameter measured on the CT monitor. The same section is shown A) scanned
in air, B) scanned in water, but with no water in the medullary cavity, and C) scanned fully
immersed. The magnitude of the AP diameter is indicated in the lower right corner of each
image.
one of the five scan locations was outlined
twice to assess the precision error of the outlining routine. Second, three pairs of femora
were CT scanned on two separate occasions
to assess the overall precision error of the
combined CT-Vicom system. The femora were
from one subadult between five and six years
old, one 25 to 29 year old male and one 45 to
49 year old female. Each scan site was
treated as a separate case to increase the
sample size. Two images could not be analyzed, resulting in a sample of 28 images.
and sign tests were used to assess the statistical significance and directionality of the
error.
RESULTS
Accuracy
The subperiosteal diameters were easily
defined, but comparability of the endosteal
diameters as measured on the CT monitor
and the actual sections with the dial caliper
was problematic because the endosteal border was difficult to define. The magnitude of
the error was small for all three techniques
Statistical evaluation
for subperiosteal diameters (Table 1). The
Accuracy and precision were calculated magnitude of the errors reported in Table 1
with the following formula:
represents about .5 mm, which approaches
the resolution of CT. The important finding
lmeasurement 1 - measurement 21 100 was that the use of a water bath eliminated
(measurement 1 + measurement 2Y2
directionality in the error for subperiosteal
diameters. When the water bath was not
Thus, accuracy and precision were calculated used, the subperiosteal diameters were conas the absolute magnitude of the difference sistently underestimated. This phenomenon
between paired measurements. Paired t tests is illustrated in Figure 3. The medullary
230
D.R. SUMNER ET AL.
TABLE I . Accuracy of computed tomography'
Scan
method'
Subperiosteal
diameters
%Error3
Ties
1.9*
1.7
1.0
1
2
3
11
4
5
+
Endosteal
diameters
% Error3
Ties
5.1*
5.1*
4.6*
1
8
7
0
0
0
1
2
2
0
1
1
+
11
9
9
'Mean percent errors for AP and ML subperiosteal and endosteal diameters are presented (n =
6 sections, with 1 AP and 1 ML subperiosteal diameter and 1 AP and ML endosteal diameter
per section). The "-"sign indicates that the CT measurement was smaller than the caliper
measurement.
'1) Scanned in air; 2) scanned in water, but with no water in medullary cavity; 3) scanned in
water, with water in the medullary cavity.
3Paired t test.
* P < .05.
TABLE 3. Precision error for the digital image
Drocessine svstem'
TABLE 2. Effect of water in medullary cavity on
calculated cross-sectional geometric variables'
Variable
AREA
IX
IY
IXnY
IMAX
IMIN
IMAXnMIN
THETA
J
% Error2
-
Ties
+
Variable
% Error2
10.2
12.6
9.1
4.0
9.1
13.0
4.0
13.4
10.8
3
1
4
0
0
0
0
0
0
0
1
1
AREA
IX
IY
IXAY
IMAX
IMIN
IXAY
THETA
0.8
1.4
1.7
0.6
1.4
1.6
0.6
0.3
3
3
3
4
1
0
4
0
2
2
2
1
4
5
1
'Mean percent errors are presented for sections scanned 1) in a
water bath with no water in the medullary cavity and 2) in a
water bath with water in the medullary cavity (n = 5).The " - "
sign indicates that the condition 1 measurement was less than
the condition 2 measurements.
'Paired t tests: no significant differences.
'Mean percent errors are presented (n = 28).
2Paired t tests: no significant differences.
TABLE 4. Precision error for the entire cross-sectional
geometric protocol'
Variable
canal diameters were consistently overestimated, and this error was not corrected by
using a water bath.
Table 2 shows the results for comparison of
the calculated geometric properties scanned
in a water bath but without filling of the
medullary cavity and with the sections totally immersed. The sample size is five rather
than six because one of the cross-sectionswas
not analyzable (due to a faulty hard disk
area). These results show that differential
filling of the medullary cavity caused an error of 4 to 13.4 percent. The area-dependent
variables (AREA, IX,IY, IMAX, IMIN,J)
tended to be underestimated when water did
not fill the medullary cavity.
AREA
IX
IY
IXnY
IMAX
IMIN
IMAX/IMIN
THETA
J
% Error2
2.6
3.3
4.3
3.6
3.5
3.3
1.9
29.3
3.3
'Mean percent errors are presented (n = 28).
2Paired t tests: no significant differences.
indicated that Scan location had no effect on
this error.
Precision error inherent in the entire protocol was evaluated by rescanning three individuals. The results are shown in Table 4.
Precision
The precision error was low for all variables
Precision error inherent in the Vicom sys except THETA, the angle between the ML
tem is summarized in Table 3. The source of axis and the principal major axis. Slight rethis error was differential positioning of the positioning errors affect THETA of cylindricursor in either corner of the water bath. The cal sections because the location of the
error was remarkably small and statistically principal axes is somewhat arbitrary in these
insignificant. One-way analysis of variance sections.
CT AND CROSS-SECTIONALGEOMETRY
DISCUSSION
The accuracy of this system, as assessed by
comparison of CT monitor measurements and
dial caliper measurements on the actual
specimens, is adequate for morphological research. Although the water bath reduced the
error for subperiosteal diameters by less than
one percent, it randomized the error with
respect to direction. Error at this surface is
particularly important because of the manner in which area moments of inertia are
calculated (see Fig. 1).Therefore, use of a
water bath or some other soft tissue equivalent is recommended when accuracy of measurement is the goal. A disadvantage of the
water bath is that it introduces another
source of error, differential filling of the medullary cavity.
We did not test the accuracy of the system
with the complete battery of variables used
in the precision tests. Such verification procedures would require digitization of photographs or contact radiographs of the cut crosssections and comparison of the calculated
geometric properties with those obtained by
CT and automated outlining. Additionally,
the effect of bone size on accuracy was not
considered.
The reproducibility of the measurement
technique was very high and was only
slightly reduced by repositioning. Precision
of CT for bone geometry was also considered
by Isherwood et al. (1976) in a n in vivo study.
As might be expected, these authors had precision errors larger than those reported in
the present (in vitro) study. Automated analysis of the digital images avoids other problems with CT, such a s defining the proper
window level and width settings and hard
copy distortion (Ruff and Leo, 1985), in addition to enhancing precision.
Computed tomography can also be used to
measure bone mineral content and density
(Revak, 1980; Genant et al., 1981). Bone density is related to the strength and stiffness of
the tissue (Carter and Hayes, 1976; 1977).
Therefore, computed tomography has the potential to determine bone geometry and infer
material properties. This is significant because the biomechanical behavior of a bone
depends upon geometric and material properties (Carter and Spengler, 1978) and this
behavior can be modeled from a n engineering perspective if loading conditions are assumed (Rybicki, 1980).
The ability to perform engineering analyses of bones based on data obtained with
computed tomography is important. Anthropologists could use this technique to under-
231
stand variation in mineral distribution and
geometry within and between species. Experimentally and clinically, the causes and consequences of bone remodeling due to altered
mechanical environments could be explored
in longitudinal research designs.
CONCLUSIONS
Computed tomography is admirably suited
to quantitative morphology for four reasons.
First, it is non-destructive to the sample of
interest. Second, it is accurate and precise.
Third, it is easily adapted to automated image analysis. Finally, computed tomography
could provide the necessary' geometric and
material property data needed for engineering analyses.
ACKNOWLEDGMENTS
This work was done at the University of
Arizona with the aid of a Comins Grant from
the Department of Anthropology to D.R.S.
Medinet, Inc. graciously donated software
and machine time on the Vicom system. This
paper was written with the support of NIH
Grant AM07375.
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